On cyclic quadrilaterals in euclidean and hyperbolic geometries

Four points ordered in the positive order on unit circle determine vertices of a quadrilateral, which is considered either as euclidean or hyperbolic quadrilateral depending whether lines connecting are lines. In case lines, this type quadrilaterals called ideal quadrilaterals. Our main result gives counterpart an earlier distances between opposite sides The proof based computations involving geometry. We also found new formula for midpoint geodesic segment disk. As application some geometric properties, we provided construction symmetrization random four with respect to diameter preserves absolute cross ratio quadruples.